The compressibility of quark matter under strong magnetic field in the NJL model

TL;DR

This paper studies how strong magnetic fields affect the compressibility of quark matter within the NJL model, revealing phase transition signatures and anisotropic behaviors influenced by magnetic field strength and temperature.

Contribution

It provides a detailed analysis of the magnetic field and temperature effects on quark matter compressibility, including phase transition signatures and anisotropic properties within the NJL model.

Findings

Compressibility decreases with increasing chemical potential and temperature.

Discontinuities in compressibility indicate phase transitions.

Longitudinal compressibility inversely proportional to magnetic field and chemical potential squared.

Abstract

The compressibility of magnetized quark matter is investigated in the SU(2) NJL model. The increases of the chemical potential and the temperature can reduce the compressibility, and lead to the much stiffer equation of state. The variation of the compressibility with the magnetic field will depend on the phase region. Due to the anisotropic structure, the compressibility is different in the directions parallel and perpendicular to the field. The discontinuity of longitudinal compressibility with the chemical potential and the temperature captures the signature of a first-order chiral phase transition and the crossover at high temperature. Moreover, the magnetic-field-and-temperature running coupling would have an important effect on the position of the phase transition. Under the lowest landau level approximation at zero temperature, the longitudinal compressibility has a direct inverse proportional relation to the magnetic field strength and the chemical potential square as $\kappa^\parallel_{\mathrm{LLL},\chi}\propto1/(eB \mu^2)$.